degree:8
 order:30
[ 8, 1, 8, 12 ][ 8, 2, 0, 0, 0, 4 ]

minimal polynomial:[ x-8, x-6, x, x+2, x+4 ] 

 minimal polynomial of other basis elements:
[ x-1, x+1 ]
[ x-8, x, x+2 ]
[ x-12, x-2, x, x+6 ]

 SITA:

[ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 8, 0, 0, 0 ], [ 1, 4, 1, 2, 0 ], [ 0, 8, 0, 0, 0 ], [ 0, 2, 0, 0, 6 ], [ 0, 0, 0, 4, 4 ] ], 
  [ [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 8, 0 ], [ 0, 2, 0, 0, 6 ], [ 0, 0, 0, 8, 0 ], [ 1, 0, 1, 6, 0 ], [ 0, 4, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 0, 0, 6, 6 ], [ 0, 0, 0, 0, 12 ], [ 0, 6, 0, 0, 6 ], [ 1, 4, 1, 4, 2 ] ] ]